I have been away a while, so this might seem to be a bit old-hat for the more regular readers, but I felt I needed to get it off my chest, so to speak (though, having read some of our more regulars, it might be pertinent): there seems to be some misunderstanding about my understanding of CO2 and its role in the atmosphere; some have called me misguided, not in full possession of all the facts, and not a scientist; the last of those is correct, the second has a high probability of being correct, and the first point might also be correct. Others have just dismissed me as a fool; another point that might be correct, but does that justify dismissal and/or vilification? Part of this misunderstanding could be because I have tried to communicate my point in few words, to reduce the chances of boring you with my missives; please humour me, and allow me to clarify my understanding in a more verbose manner, and I would welcome correction on any points where you consider me wrong. Just telling me that I am wrong, without explanation, will be of no help whatsoever to anyone, least of all myself, and I feel justified in recommending that anyone who attempts that be ignored, else there could be some risk of derailing the discussion. Please bear in mind that I might feel obliged to partake of rather pedantic definitions, knowing that there are some who might be reading who will take great delight in unpicking every slight nuance, while ignoring the general thrust of the discussion.

The fact that CO2 can act as a “greenhouse gas” – i.e. absorbs energy from radiation (in this case, in the infra-red end of the spectrum) – is not disputed. It has been witnessed in laboratory experiments, where the contents of a closed container enriched with CO2 rises in temperature faster than a control closed container of ordinary air when both have been subjected to infra-red radiation (similar experiments have also shown this to fail, but let us ignore those, for now). However, that this phenomenon has such an effect that CO2 becomes the key driver of atmospheric temperature has to be doubted.

Reasons for this doubt: (1) CO2 exists as a minute proportion of the atmosphere; thus, for it to imbue a noticeable increase of heat energy into the atmosphere, each molecule would have to absorb a remarkable amount of radiative energy. This absorption could be enhanced if CO2 was an attractor for the outgoing radiation – an IR magnet, so to speak – but that is an absurd idea. This absorbed energy would then need to be distributed to the surrounding air molecules via conduction and convection, as well as re-radiating part of it, less than half of which would be downwards. At present concentrations, each CO2 molecule would have to share this energy with an average of at least 2,500 other air molecules. This suggests that an awful lot of energy is required for it to have a noticeable effect over such dispersal.

(2) There are other “greenhouse gasses” extant within the atmosphere, many of which having been shown to be more effective than CO2 (with some considerably so) at absorbing radiative energy, and at least one of these existing in far greater concentrations than CO2; why are none of these considered to have an impact as significant as that claimed for CO2?

(3) Bearing in mind the “environmental sensitivity” being xK per doubling of CO2, what would be the calculated temperature if Earth’s atmosphere was 99% CO2? This is a little more than an 11-fold doubling (11.27) of present levels (rounded to 0.04%), thus giving us a theoretical temperature rise of about 11xK; thus, if x = 1, global temperatures would rise at least 11K. (3a) What was the average global temperature when CO2 concentrations were about 4,000ppm, ten times present concentrations, or somewhat under 7 doublings (i.e. 6.65)? Is there evidence that it was more than 6xK the present average? Why were the Minoan, Roman and Mediaeval Warming Periods as warm as or warmer than today, when CO2 levels are generally agreed to have been lower? If x is a real number, then logic dictates that they should have been cooler than the present.(3b) Venus has an atmosphere that is about 96.5% CO2 (11.24 doublings). At an altitude where the atmospheric pressure on Venus is the same as Earth’s (1,000mb), the average temperature is about 66°C, which, it has been calculated, is what the Earth’s atmosphere would be, were its orbit the same distance from the Sun as Venus’s. Why is the Venusian atmosphere at this altitude at this temperature, and not ~77°C (or (66+11x)°C)? All this suggests that either the “environmental sensitivity” is considerably lower than continues to be thought (not less than 1K, but perhaps as high as 4.5K, though these figures continue to trend downwards), or that the “greenhouse effect” theory is wrong. Occam’s Razor, whereby the simplest explanation is the most likely to be the correct explanation, suggests to me that it is the latter of these. And, finally:

(4) CO2 concentrations in the atmosphere continue to rise, while temperatures do not.

Possible explanations for a warm atmosphere? My guess (ref: Richard Feynman) is that it is a combination of many things, such as, but not limited to: the application of the gas laws; conduction of surface heat to the air in contact with it; and convection of said heat – which vultures and other gliders take great advantage of, which does indicate that there is some serious energy involved. With convection, there is movement; with movement there is friction; with friction, there is heat – this will be minimal, and may not actually be measurable, which, I would moot, puts it in the same category as the “greenhouse gas” effect – perhaps there, possibly influential, but not measurable. That said, I would also guess that radiated heat is more likely to be intercepted by particles, solid and/or liquid, in the atmosphere, as they are far larger than molecules, thus presenting a far greater surface area to intercept the radiated energy, they probably exist in far greater quantities than most of the supposed greenhouse gasses, and absorb a broader spectrum. However, the greatest absorption of the heat is from the top down, with the atmosphere directly absorbing the energy of the Sun. The reason the sky is blue has been shown to be because of particles in the air absorbing some of the visible solar radiation (a.k.a. light); that it is blue does suggest that it is the red end of the spectrum that is being absorbed. The red end of the spectrum is where the heat is (hence the use of infra-red lights in the experiments mentioned in the second paragraph); this red light has been absorbed – where has its heat gone? Teleported, perhaps, into the deep, deep oceans? If so, why has it waited until recently to turn that mechanism on?

Another good example that supports this guess is a clear, cloudless night, especially if there is no air movement. While the quantities of greenhouse gasses remains more-or-less constant (less so with water vapour, admittedly), the temperature plummets. If there are particles in the atmosphere, such as dust, mist, fog (i.e. denser mist) or clouds, then the temperature fall is considerably less. Anecdotal support: I have slipped on ice formed from a trail of water from a leaking tap; it was early in the morning after a very clear, cloudless night in the Persian Gulf. While the air temperature was observed to be in double figures (and the man with me expressed no cold discomfort, dressed in shorts and short-sleeved shirt), the surface, evidently, was not.

This supports yet another guess – the vast majority of the atmosphere comprises of nitrogen and oxygen; both of these are acknowledged as being very poor absorbers of radiative energy. My understanding is that if something is a poor absorber of radiation, it is also a poor emitter of that radiation, thus both gasses are good retainers of heat when the principal heat source is removed (i.e. it is night-time); cooling of the air occurs when the turbulence of air movement causes loss of heat through conduction with cool surfaces. In the anecdote given above, the air had been remarkably still, so ensuring that there was little, if any, turbulence for the air not in contact or close to contact with the ground to be able to lose its heat through conduction; hence the air temperature at human-height seemed warm, yet the surface temperature was not, the surface having radiated its energy virtually unimpeded through the clear air during the night.

Without wishing to bore you yet further, I suppose I had better leave it, there.

A definition of "too long; didn't read." 1. The inability to accept, understand or pay attention to information when not separated by a header. 2. The ability to arbitrarily read 400 small posts but not a long one. 3. A sign of ADD or lack of reading capability. 4. A very cheap response and an indication of lack of wit. 5. 90% of the time: A lie. 6. A desperate attempt at a comeback used by people who just can't think of one. 7. Usually used by people who've been torn apart verbally but want one last attempt at looking witty. 8. Total failure at #7. 7. A sign that, not only is someone too lazy and stupid to read but, clearly, too lazy and stupid to even type out four words indicating such. 9. Collect every "tl,dr" post online, and you'll have a good estimate of the number of lazy idiots on Earth, who currently have Internet access. 10. Should really be: "Too Lazy, Don't Read." or, ".....I got nut'n!"

Thank you, BoFA (such an apt name). One of the problems that I have encountered is trying to get as much meaning into as few words as possible; it doesn’t always work. The downside to a full explanation is that it can look scaringly long. Aware of that, I have tried write it to be easier to read than many of the papers often cited; whether I have succeeded or not is only for others to judge.

(1) CO2 exists as a minute proportion of the atmosphere; thus, for it to imbue a noticeable increase of heat energy into the atmosphere, each molecule would have to absorb a remarkable amount of radiative energy.

But is that how it is supposed to work? Forgetting about "CO₂ traps heat", the basic mechanism is argued to be:

- Little of the IR from the Earth's surface gets radiated direct to space due to the opacity of the atmosphere to longwave IR. Only from the upper regions of the atmosphere do IR photons finally escape to space without further interaction with the atmosphere.

- Increased CO₂ means that the mean height from which IR escapes is increased, because the opacity of the atmosphere to IR has been increased. The lapse rate, in °C/km, being fixed (allegedly), means that radiation from space now occurs from heights where the temperature is lower, so the outgoing radiated power is reduced. The difference between the new outgoing power and the power of the incoming radiation is the so-called "missing heat". [Or, once the system has again reached equilibrium, the ground temperature has to have increased so that the outgoing longwave IR power equals the power of the incoming solar radiation.]

Voila, the greenhouse effect in a nutshell.

My own guess is that "the missing heat" is simply not there. The only 'evidence' for it computations by unvalidated models, as the difference between incoming and outgoing from satellite measurements is dominated by measurement error.

The assumption of a strict proportionality between height and temperature seems an oversimplification even within the troposphere. And any radiation to space from the stratosphere is clearly not governed by the assumption of a constant lapse rate.

(3) Bearing in mind the “environmental sensitivity” being xK per doubling of CO2,

Some time back, I tried to track down the origin of the supposed logarithmic relation between CO₂ concentration and so-called 'radiative forcing'. Simple analytical formulas normally result from some fundamental physical effect - for example the logarithmic relation between voltage and forward current in a semiconductor diode which holds over a huge range of currents - eight or nine orders of magnitude (from memory).

In the end, SoD pointed out that it comes from the Myhre et al paper (GRL, vol 25,pp 2715-2718, 1998) where a log curve was numerically fitted to the results from numerical calculations over a limited range. So it is more an empirical result over a limited range, rather than a formula resulting from some fundamental principle. Steve McIntyre (I think) pointed out that a square root formula would fit the numerical points just about as well.

Bottom line. In the absence of a firm reason to expect the logarithmic relationship to hold over a wide range, it's a mistake to assume it should apply.

Increased CO₂ means that the mean height from which IR escapes is increased, because the opacity of the atmosphere to IR has been increased.

Yes but, as RR says,"CO2 exists as a minute proportion of the atmosphere."The actual concentration of CO2 may well have increased by 33% but given that it was a very, very small part of the greenhouse gas content to begin with that effect must be commensurately small, one would imagine. If we assume (for the sake of argument since I don't know what the actual figures are) that CO2 accounted for 1% of the greenhouse gas content prior to 1850 it now accounts for ~1.1% and on that basis I would have thought that any effect it is likely to have on any aspect of climate is lost in the noise.I'm with RR on this one. I simply fail to understand how such a minute variation in the total concentration of greenhouse gases can have the effects that are being attributed to one very small component of them.

Thank you, Martin A. So, the theory is that increasing CO2 effectively increases the opacity of the atmosphere, leading to greater heat retention. An analogy could be the heat within a room being retained by the glass of a window; CO2 is a fly-speck on that glass, and so increasing its effectiveness in retention. Quite why this fly-speck could have the dramatic effect that is claimed is what grates with me. My own inclinations are to agree with you – the “missing heat” is not there.

So, the theory is that increasing CO2 effectively increases the opacity of the atmosphere, leading to greater heat retention.

I said "because the opacity of the atmosphere to IR has been increased".

I now think it would have been much better had I said "the height at which the atmosphere is becomes not completely opaque has been increased". Both before and after the addition of CO₂, the atmosphere was pretty well opaque up to a certain height. What changed was the height at which it became transparent increased.

[I think the window+fly speck analogy is probably misleading. I could come up with an alternative analogy (eg 1/8" of transparent glass, with a 1/1000" layer of aluminium but where the reflection was due almost 100% to the aluminium) but that would be misleading too.]

The key thing to understand is the effect of the lapse rate and the height at which radiation finally leaves for the far corners of the universe.

MJ - I don't carry in my head the total effect of CO₂ relative to other greenhouse gasses but, though minor, it is not negligible. (I'll have to look it up but I'm preparing for a trip and may not do it for quite some time).

If it happened to be correct that CO₂ has increased from 280ppmV since pre-industrial times to 400ppmV now, then the proportion change would be more than from 1% to 1.1% .

If it were 1% pre-industrial, it would now be 1 × 400/280 per cent = 1.4%. Have I got that right?

for example the logarithmic relation between voltage and forward current in a semiconductor diode which holds over a huge range of currents - eight or nine orders of magnitude

Also from memory. Diodes, forward biasing starting at 0V produces very little current until the barrier voltage is reached (0.7V volts in Silicon and and about 0.3 in Germanium) at which point the current increases rapidly, There is a knee in the curve at that point. To my mind that would be the opposite to atmospheric CO2, where whatever CO2 does to average global temperature "rapidly" increasing levels at > 240 ppm are having no effect. At levels <200ppm who knows as we never seem to have gone that low.

Bottom line. In the absence of a firm reason to expect the logarithmic relationship to hold over a wide range, it's a mistake to assume it should apply.

This seems entirely reasonable, from the limited evidence available there appears little or no relationship historically.

Martin AYour calculation is probably right. I'm afraid decimal fractions have always been a bit of blind spot. My argument really is that CO2 is itself a very small part of the greenhouses gases but is treated, at least for "political" purposes as if it were the major driver. I would probably be making more sense if I knew what the concentration of all the greenhouse gases was. Not that I haven't tried to find out but since no site I have yet been to gives a figure for water vapour it's a bit hard to put the others in any sort of perspective.

TBYJThanks for that.However, it sets me off on another quest.1. How do you measure that effect? (And if 20-30% really is as far as they've managed to pin it down I'm not all that confident.)2. How does a molecule of CO2 absorb photons any differently from any other molecule that absorbs in the infra-red?

And it seems to me that, unless CO2 molecules take up a lot more space than e.g. water vapour molecules then that photon still has the same 2,499 chances out of 2,500 of missing altogether.

MartinA, I have always assumed that the logarithmic relationship is derived from the Beer-Lambert law, which I have no problem with. But, as is often repeated, this is only the first or second step in long branching chains of reasoning about cause and effect.

SandyS - I did not intend to imply there was any analogy whatever between atmospheric CO₂ and semiconductor diode behaviour. I chose the latter as an example of where a theoretical calculation *does* yield a log formula - and one that hold over a wide range, even with actual devices.

The analogy would be [diode current:CO₂ concentration], [diode voltage:global temperature rise] so that progressively bigger increases of current are needed to get constant increases in voltage drop. But I don't think it's an analogy of any value.

You are right about Ge and Si diodes. It's what pops out of the formula. (Have you come across the use of LED's is to get diodes with higher voltage drop than with silicon in wavefrom shaping circuits? I think a blue LED needs about three volts to conduct - the equivalent of around five silicon diodes in series.)

Looking up the diode equation, although I should have been able to quote from memory:

What's I₀ for a silicon diode? Dunno offhand but a small fraction of a microamp. So, for I to be a significant current (milliamps, for example), exp(qV/kT) has to be very big, since it is multiplied by the tiny I₀.

With exp(qV/kT) being much greater than 1, we can neglect the 1 and take logs of both sides of the equation: log I = log I₀ + qV/kT

Hold on! Haven’t you gone a bit off-topic, here? How does the formula for diodes equate to CO2, the evil greenhouse gas? As analogies go, it is a rather desperate ploy (somehow, my fly-speck seems so much more appropriate)!

Are there any estimates (proxy readings) for temperatures when CO2 concentrations were more than 6 doublings of present levels? I would moot that, if there are, and they are NOT 6xK higher, then the idea that CO2 is the dominant factor in atmospheric temperatures is dead in the water, and the very principle of “greenhouse gas” is holed below the water-line.

RRI think it was a minor diversion rather than a complete re-routing. The actual point was provable logarithmic relationships.

The best we've managed in finding out where it comes from in the case of atmospheric CO2 is michael hart's reference to Beer-Lambert Law which is to do with attenuation of light passing through a material. How this works in an atmosphere with variable content no one has stated clearly. Particularly with the water vapour content which has absorption in the same IR band. By the same principle water vapour will be logarithmic also?

RR - You had kicked off with discussion (amongst other things) of what happens per doubling of CO₂. That implies there is a logarithmic relationship, so the discussion found its way to such relationships.

The formula for change in radiative forcing for a given change in CO₂ (that Entropic Man seems to regard as as well established as something that has been well established) is delta F = 5.35 log (C/C₀).

The formula for the voltage across a diode is V = constant × log (I / I₀). The formulas are similar, so not unreasonable to ask if there is an analogy between CO₂ and diodes that might give insight. Hence the brief discussion.

I think you may have conflated greenhouse effect with AGW. The first is real and the second is the contentious point.

Greenhouse Effect:A planet with an atmosphere of non-radiative gasses will radiate to the sink of space from its surface only.That same planet, but with an atmosphere including radiative gasses, will radiate to the sink of space from surface and atmosphere.In both those scenarios, the average radiating temperature will be the same.In the second scenario, the average temperature at the surface will be higher than the average radiating temperature. That phenomenon has two climate science explanations. The first is that it is the effect of the gas laws and gravity and the second is that back radiation from the atmosphere is the cause. In either case, GE is not anthropogenic.

AGW:From the two GE explanations, a dynamic effect from continual increases in radiative gasses is hypothesised for each. Both conclude that an imbalance between outgoing and incoming solar radiation will occur and the result of that will be an accumulation of energy leading to higher temperatures.

The direct effect has been calculated as 1 deg C per doubling of CO2. That has not been changed even though estimates of a 0.9W/m^2 energy imbalance have been lowered to 0.6W/m^2. Attempts have been made to measure the imbalance using satellite mounted sensors. Neither a static or dynamic imbalance has been found.

Looking at the radiation budget hypothesis (the Trenberth diagram) you will find energy flows within the system greater in magnitude than that entering and exiting it. The potential for those flows is there because those radiation levels have been measured. The key word is potential because it is necessary to measure the opposing radiation levels to find the difference which then gives the actual kinetic magnitude and direction. A simple experiment shows the radiation budget hypothesis to be false: measure the radiation from the direction of the horizon at two points of the compass 180 deg apart and subtract one from the other and you will find the answer to be zero. You have measured the potential, not the kinetic energy. As the two readings have come from the same temperature the flows have canceled. The hypothesis is bust.

Looking at the alternative explanation, it is hypothesised that as more radiative gases are added to the atmosphere, radiation from it will move higher on average and as higher in the atmosphere is colder then the total of outgoing radiation will reduce. Therefore energy is accumulating. That conclusion is drawn without any consideration of area of radiation which will itself have increased with height (or that higher is colder is not true for all heights in the atmosphere). An increase in area would cause an increase in radiation to space and a reduction in any imbalance. The hypothesis is incomplete and therefore bust.

CAGW:This is what turns climate science from an esoteric study into something of general interest. Looking first at its predictions of where we should be now we find that they have failed. Explanations (consensus) for that are not mea culpa but post hoc. Currently, climate science is fooling itself.

Ssat: I have no trouble with the “greenhouse effect”, as it seems logical that the atmosphere will retard the radiation of energy to space. That a “greenhouse gas” is required for this is where I balk; I find it difficult to accept that a gas that exists in very small quantities could have such an impact. What happens in the Persian Gulf in summer time is, with the inter-tropical convergence zone (ITCZ) moving over the region, it gets covered by a thermal inversion – where the temperature stops cooling with height – and the heat gets trapped, leading to what can be quite dangerous air temperatures (sea-level temps of 40+°C are common; 50+°C can occur) coupled with high humidity; a good analogy would be to liken it to the lid on a pressure cooker. In the anecdote I gave (occurring in the winter), all that was lacking in the atmosphere was particles (liquid or solid), and exceptionally still air. To replicate the anecdote, all that would be required would be to surround an area of desert (preferably of dark colour) with a high wall, to minimise air movement over the ground, cover the ground with a thin layer of water and then sit back and wait for a clear, cloudless night. Curiously, when I was at school, this is what I was told was a common way of getting ice in Arabia.

I conclusion, I do agree with you: climate science is fooling itself – which would be no great shakes in a real world, but we no longer live in a real world; we live in the world of Mann, Dibble, Yeo and other assorted troughers, which is even more ludicrous than any that Lewis Carroll or others could possibly envisage, and climate “science” is fooling everybody.

Radical : "I find it difficult to accept that a gas that exists in very small quantities could have such an impact."

For a CO2-free expanation of GE see yesterday's posting at the Hockey Shtick.

Without back-radiation as any part of the explanation for GE, why invoke it for AGW? Perhaps increasing the mass of a radiative atmosphere by 100 ppb will have a comensurate tiny effect on what we experience living at the bottom of it?

ssat: "That conclusion is drawn without any consideration of area of radiation which will itself have increased with height (or that higher is colder is not true for all heights in the atmosphere). An increase in area would cause an increase in radiation to space and a reduction in any imbalance."

Do you really think you (or whoever you copied that from) thought of areas and heights first? It is easy enough to calculate the surface area of a sphere. Why didn't you do that before writing such nonsense? With a lapse rate of -10 C/km, a surface temp increase of 1C will increase the radius to the effective radiating surface by 100m. The earth has a radius of 6371km. Add maybe 20km to get to the effective radiating height. The surface area is 513'000'000 square kilometres. Adding 100m increases the area by 16'000 km2. That is an 0.003% increase, which is like adding an area of skin the size of a finger nail to your body - and you think that is going to make a difference.

As far as I'm aware, inversions are transient, local effects at relatively low altitudes. I doubt they have any overall effect on IR emissions.

"I find it difficult to accept that a gas that exists in very small quantities could have such an impact."

That has to be one of the many myths listed at SKS. Maybe you should go read them. Oxygen, nitrogen and argon, which make up more than 99% of the atmosphere, are not radiatively active and so can be ignored when it comes to IR radiation to space (the only way the planet keeps cool). CO2 and water vapour make up most of what is left, and at altitude there is very little water vapour. So CO2 is not in such small quantities. These are commonplace facts not black magic climate science.